My Small Research

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As one of the lesson subjects in school, mathematics has an important role to build students’ thinking. It’s not a lie. Mathematics school gives an impact for students although they don’t realize clearly. When we talk about mathematics, we should discuss about mathematical thinking too. I am curious with senior high school students’ mathematical thinking. I would like to know how far they understand about the content of mathematics that they’ve learned, how they build their competence in mathematics, and how they love mathematics. That’s the reason why i made a small research related to mathematics psycology.

Based on Katagiri (2004), mathematical thinking has many characteristics. First, Focus on Sets
Mathematical thinking is like an attitude, as in it can be expressed as a state of “attempting to do” or “working to do” something. It is not limited to results represented by actions. Second, Thinking Depends on Three Variables. it means the way of thinking depends on three variables: the problem (situation), the person involved, and the strategy. Third, Denotative Understanding. Even the concept of mathematical thinking is expressed with words, but it should be shown with concrete examples. Fourth, Mathematical Thinking is the Driving Force.

Still from Katagiri (2004), mathematical thinking has three types. First, Mathematical Attitude. It is related with students attitude in learning mathematics. It can be their curiousity with mathematics, their motivation to learn mathematics, etc. The second type is mathematical method. This type is related to how the students solve mathematics problem, what kinds of method that they use, etc, and the last is mathematical content. It shows the students understanding in materials and how far they can develop their ability in real life.

In this research, I had three respondents. They have good and closer relationship with me. First, I would like to describe them.

1. Akhmad Akbar (1^st grade of Muntilan Senior High School). He is my little brother. He has good competence in mathematics but he’s lazy. He studies mathematics rarely. He thinks if he understands, he shouldn’t learn more. He just studies when there will be a test or when he has assignments. It makes him don’t get maximal results.

2. Ayu Wulandari (2^nd grade of SMKN 1 Salam). She is my neighbor. She is average students. Truly she doesn’t have good ability in mathematics. But she is interested to solve mathematics problem when she get a task. She always tries to do it. Even, she would ask me when she couldn’t do it.

3. Akhmad Wildan Listyanto (2^nd grade of Kota Mungkid Senior High School). He is my cousin. He is in natural science major. He has average ability but he is diligent. So he can understand the material well. He has a regular time to study.

I have seen their development in mathematical thinking for a month. With the different characteristics that they show when they learn mathematics, they got different results in their 1st semester report. Akbar didn’t get maximal results because he didn’t study hard. He just got 75. It isn’t like what he should get. Ayu got 60. She studied hard, but she had low understanding. It made she couldn’t get good result. Then Wildan got 79. Those comparation shows that every person has different ability, different way, and different result when he/she learn mathematics.

I also gave some questions to them related to their learning in mathematics.

1. Do you like mathematics?

2. What can make you motivated to learn mathematics?

3. What is your favourite material?

4. What is the difficulty that you find when you learn mathematics?

5. Do you have special time to learn mathematics?

6. What is the method that you use to understand the content of the material?

Their answers are:

Akbar  

1         He likes mathematics very much

2    The teacher and the materials

3    Exponential  

      He can’t read the mathematics language well  

5    No  

6    Listen the teacher’s explanation then understand it at the same  

Ayu

She likes mathematics

Because mathematics is one of school lesson

She doesn’t have favourite material

She can’t find the concept of materials quickly

Sometimes

Need others help to explain the material.

Wildan

He likes mathematics

Because mathematics is difficult

Statistics

He gets difficulties when he learns about trigonometry

Yes

Read the material seriously. Then do some exercises to time understand in depth.

Based on the research that i’ve done, i got information that SMK students have different view with senior high school students. Ayu likes mathematics because it is one of the school lesson. On the other side, Akbar and Wildan like mathematics because they are interested with mathematics unique. The difficulty that always happen in senior high school students is when they have to change the problems into mathematics language. They are difficult to visualize the abstract concepts that it make them don’t get full concepts in their mind. I also can compare the students thinking from different grade. I find that the higher grade student has more awareness to learn mathematics although they don’t understand well. On the other side, some students which is in lower grade learn mathematics when they get tasks or tests.

I think the phenomena above show that students in senior high school still need motivation and awareness to learn mathematics. They also need more realistic example when understanding the material.

The Power of Category and Networking

Human mind consists of many aspects, such as quality, quantity, category, relation. Those aspects are used to value about an object from many points of view. We can value the quality of an object, categorize it in a certain group, and make a relationship between this object and the other object that we’ve ever known. Immanuel Kant (1771) stated that our mind has abstraction, idealization, intension and epoche. Abstraction means learn something which is important to learned. Idealization means assume that something is perfect. Intension comes from our awareness. And epoche is a place to save unimportant things or a place to hide something that we don’t want to think on a certain time.
In mathematics education phenomena, we should use categorization to divide what characteristics which is in abstraction or epoche. Categorization means put an object in a group which is suitable for it. With categorization, we can learn mathematics easier because we’re helped to choose what we should learn. For example, when we learn about cube, we don’t need to know what its material, what its form, what its price. We just learn its size, its length, its width.
This world consists of Noumena and Phenomena. A phenomenon is something that is real. To make the phenomena become knowledge. We need a good thinking from bottom and from upside. Learning can be done by two methods. First, bottom up method. We learn from a real thing then we get a new concept from it. Second is top down method. We learn from some references like books, journals, research reports to get some theories then we practice them in our real life. Both of them are very useful for us.
Besides learning methods, we also have learning system. There are routine, intensive and extensive. We learn routinely when we learn based on the given schedule. We learn intensively when we learn from the general to specific. And extensive learning happens when we learn from the specific to find the general form.
Students who learn mathematics have mathematical thinking. It consists of mathematical attitude, mathematical method and mathematical content (Katagiri,2004). Those aspects have a relationship with the nature of school mathematics. Making a pattern, solving a problem, investigating and communicating need attitude, method and content. That’s why categorization and networking are very important for us. Categorization helps us learn easier and make networking will help us to combine and relate the knowledge that we’ve ever got. From that, we can make a theory then try to prove it. we can find the evidences using analysis.